# Multivariate Nonlinear Regression
**URL:** https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887
**Category:** Optimization (Mathematical)
**Created:** [July 1, 2019, 7:13am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887 "2019-07-01T07:13:58Z")
**Posts on this page:** 10
**Page:** 1
### Author:  [@MLackner](https://discourse.julialang.org/u/MLackner)
#### Post date: [July 1, 2019, 7:13am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/1 "2019-07-01T07:13:58Z")
Greetings!
I am trying to perform a multivariate nonlinear regression (2D curve fitting). Let’s assume my data has the following form:
```julia
function multimodel(x, p)
a = x[1]
t = x[2]
α = p[1]
τ = p[2]
(α .* a) * (τ .* (t.^2)')
end
t = -1.0:0.1:1.0 |> collect
a = 0.0:0.1:1.0 |> collect
p = [0.9,1.1]
x = [a, t]
y = multimodel(x, p) + 0.1 * rand(length(a), length(t))
using PyPlot
mesh(t, a, y)
```
Which gives the following noisy data:
I tried fitting using `LsqFit`:
```julia
using LsqFit
fit = curve_fit(multimodel, x, y, [1.0, 1.0])
```
which results in
```plaintext
MethodError: no method matching isinf(::Array{Float64,1})
```
I have to admit that that’s not how the `LsqFit` documentation says how their multivariate regression works. In there it states:
> There’s nothing inherently different if there are more than one variable entering the problem. We just need to specify the columns appropriately in our model specification:
> `@. multimodel(x, p) = p[1]*exp(-x[:, 1]*p[2]+x[:, 2]*p[3])`
But I don’t quite understand that because the arrays of the two independent variables must have the same length? And I don’t get a 2D array out of that function.
I also tried modelling my problem with `JuMP` but I didn’t get very far there.
Does anyone have some experience with this kind of curve fitting?
---
### Author:  [@pkofod](https://discourse.julialang.org/u/pkofod)
#### Post date: [July 1, 2019, 8:19am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/2 "2019-07-01T08:19:06Z")
I’m not sure what you’re doing exactly.
Do you want to do non-linear least squares, or do you want to interpolate?
---
### Author:  [@slowbrain](https://discourse.julialang.org/u/slowbrain)
#### Post date: [July 1, 2019, 8:58am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/3 "2019-07-01T08:58:40Z")
it seems that wrong argument is passed to `isinf` by `curve_fit` somewhere along the way
try to overload `isinf` to cover `isinf(::Array{Float64,1})` case and see it you get something reasonable out of the fit
---
### Author:  [@slowbrain](https://discourse.julialang.org/u/slowbrain)
#### Post date: [July 1, 2019, 9:12am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/4 "2019-07-01T09:12:14Z")
disregard my suggestion, no use… I’ve tried to overload `isinf` and `isnan` but ended up with `ERROR: StackOverflowError:` with no details
---
### Author:  [@MLackner](https://discourse.julialang.org/u/MLackner)
#### Post date: [July 1, 2019, 9:23am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/5 "2019-07-01T09:23:18Z")
The plan is to do nonlinear least squares fitting.
---
### Author:  [@feanor12](https://discourse.julialang.org/u/feanor12)
#### Post date: [July 1, 2019, 9:26am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/6 "2019-07-01T09:26:03Z")
In the readme of LsqFit they pass a 2d array as x. I think you passed an array of arrays.
@. multimodel(x, p) = p[1]\*exp(-x[:, 1]\*p[2]+x[:, 2]\*p[3])
---
### Author:  [@MLackner](https://discourse.julialang.org/u/MLackner)
#### Post date: [July 1, 2019, 10:19am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/7 "2019-07-01T10:19:34Z")
> [@feanor12](#):
>
> In the readme of LsqFit they pass a 2d array as x. I think you passed an array of arrays.
>
> @. multimodel(x, p) = p[1]\*exp(-x[:, 1]\*p[2]+x[:, 2]\*p[3])
This is where I don’t get the readme. If I pass a 2D array the first thing is that my independent variable arrays have to have the same length which they don’t have. And secondly that the `multimodel` function from the readme returns a 1D array instead of a 2D array.
---
### Author:  [@feanor12](https://discourse.julialang.org/u/feanor12)
#### Post date: [July 1, 2019, 11:46am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/8 "2019-07-01T11:46:56Z")
maybe try something like this
```julia
function multimodel(x, p)
a = x[:,1]
t = x[:,2]
α = p[1]
τ = p[2]
@. α * a * τ * t^2
end
a = []
t = []
trange = -1.0:0.1:1.0
arange = 0.0:0.1:1.0
for _t in trange , _a in arange
push!(a,_a)
push!(t,_t)
end
p = [0.9,1.1]
x = [a t]
y = multimodel(x, p) + 0.1 * rand(size(a,1))
using Plots
Plots.plot(a,t,y,seriestype=:surface)
```
---
### Author:  [@MLackner](https://discourse.julialang.org/u/MLackner)
#### Post date: [July 1, 2019, 11:56am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/9 "2019-07-01T11:56:58Z")
> [@feanor12](#):
>
> maybe try something like this
> […]
Yes! This works! That really helps a lot. Thank you! 🤩
---
### Author:  [@pkofod](https://discourse.julialang.org/u/pkofod)
#### Post date: [July 2, 2019, 11:44am UTC](https://discourse.julialang.org/t/multivariate-nonlinear-regression/25887/10 "2019-07-02T11:44:01Z")
Okay, now I see what you wanted to do. Do you realize why the suggestion worked?
To use LsqFit you need to provide a number (N) of _observations_. In your case, the observations are chosen by you: you want to sample a the full tensor grid defined by two (in this case) vectors. Then you have to consider each combination/point as one observation. This obviously means that some `a`s are going to be repeated for some `t`s and vice versa. This is the part I didn’t understand when you said “why do a and t have to be of the same length” - well because you need N pairs!